Flow over an airfoil

AIM: To simulate flow over a NACA 0012 airfoil and find its stall angle for a given Reynolds number.

GEOMETRY DESCRIPTION:

• NACA 0012 airfoil
• Chord length: 1m
• Span: 0.5m
• Tip type: Square tip

COMPUTATIONAL DOMAIN:

Upstream length: 5m

Downstream length: 15m

Top and bottom length: 7.5m

SIMULATION TYPE: 2D

OPERATING CONDITION:

• Reynolds number= 6.88e5
• 1 atm pressure

PROCEDURE:

• Create the airfoil by inserting the coordinates as a curve
• Extrude the sketch using midplane extrude
• Save the part
• Open flow simulation from add-ins
• Open wizard
• Setup an external flow
• Input fluid as air
• Setup operating conditions
• Specify inlet velocity in x direction as 10m/s
• Give appropriate mesh parameters
• Setup all plots and goals
• Run a simulation until the mesh is found to be independent
• Carryout the same simulation for different angle of attacks and determine the stall angle

RESULTS AND DISCUSSIONS:

Angle of attack: 0°

The solver was setup and the mesh dependency test was performed until the lift force value was found to converge to 0. This is because, the chosen airfoil is symmetric and would have 0 value for Coefficient of lift at 0° angle of attack. Hence this is the parameter based on which the mesh could be validated.

The Lift force was found to be 0, which physically agrees.

Angle of attack: -2

Angle of attack: -4

Angle of attack: -6

Angle of attack: -8

Angle of attack: -10

Angle of attack: -12

Angle of attack: -14

Angle of attack: -16

Angle of attack (°)	Drag force (N)	Lift force (N)
0	0.072	-0.006
2	0.078	1.179
4	0.098	2.305
6	0.125	3.459
8	0.183352	4.38554
10	0.26689	5.37823
12	0.38278	5.87202
14	0.730651	4.09689

From the above graph, we see that the value of lift force drops at an angle of 14°, hence the stalling angle for the NACA 0012 airfoil experiencing a Reynolds number 6.88e5.

From the above graph it is observed that the increment of the Drag force is higher once the airfoil reaches stalling condition.

From the drag and lift forces, we can compute the `C_d` and `C_l` values as:

`C_d=(2D)/(ρ.A.V^2 )`

`C_l=(2L)/(ρ.A.V^2 )`

The area (A) is the frontal area, which was calculated by projecting the airfoil in a plane perpendicular to the direction of flow velocity.

A= 0.12*0.5 m²

A= 0.06 m²

The and values are:

Angle of attack	`C_d`	`C_l`
0	0.024	-0.002
2	0.026	0.393
4	0.032666667	0.768333
6	0.041666667	1.153
8	0.061117333	1.461847
10	0.088963333	1.792743
12	0.127593333	1.95734
14	0.243550333	1.36563

The `C_d` and `C_l` values were compared to a wind tunnel test of the same airfoil having same dimensions and are found to be of the same order.